Question: Simplify. Remove all perfect squares from inside the square root. Assume $y$ is positive. $\sqrt{200y^4}=$
Explanation: Factor $200$ and find the greatest perfect square: $200=2\cdot 2\cdot 5\cdot 5\cdot 2=10^2\cdot 2$ Find the greatest perfect square in $y^4$ : $y^4=\left(y^2\right)^2$ $\begin{aligned} \sqrt{200y^4}&=\sqrt{10^2\cdot 2\cdot \left(y^2\right)^2} \\\\ &=\sqrt{10^2}\cdot \sqrt{2} \cdot \sqrt{\left(y^2\right)^2} \\\\ &=10\cdot \sqrt{2} \cdot y^2 \\\\ &=10y^2\sqrt{2} \end{aligned}$